Problem: Solve for $x$ and $y$ using elimination. ${-5x+y = -17}$ ${-3x+4y = 17}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ ${20x-4y = 68}$ $-3x+4y = 17$ Add the top and bottom equations together. $17x = 85$ $\dfrac{17x}{{17}} = \dfrac{85}{{17}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-5x+y = -17}\thinspace$ to find $y$ ${-5}{(5)}{ + y = -17}$ $-25+y = -17$ $-25{+25} + y = -17{+25}$ ${y = 8}$ You can also plug ${x = 5}$ into $\thinspace {-3x+4y = 17}\thinspace$ and get the same answer for $y$ : ${-3}{(5)}{ + 4y = 17}$ ${y = 8}$